Factors, Multiples and Primes - Short Problems

A collection of short Stage 3 and 4 problems on factors, multiples and primes



Weekly Problem 10 - 2008

Stage: 3 and 4 Challenge Level: Challenge Level:1

If the numbers 1 to 10 are all multiplied together, how many zeros are at the end of the answer?

Weekly Problem 14 - 2008

Stage: 3 and 4 Challenge Level: Challenge Level:1

The numbers 72, 8, 24, 10, 5, 45, 36, 15 are grouped in pairs so that each pair has the same product. Which number is paired with 10?

Weekly Problem 22 - 2008

Stage: 3 and 4 Challenge Level: Challenge Level:1

The following sequence continues indefinitely... Which of these integers is a multiple of 81?

Weekly Problem 26 - 2008

Stage: 3 and 4 Challenge Level: Challenge Level:1

If $n$ is a positive integer, how many different values for the remainder are obtained when $n^2$ is divided by $n+4$?

Weekly Problem 41 - 2008

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

How many pairs of numbers of the form x, 2x+1 are there in which both numbers are prime numbers less than 100?

Weekly Problem 1 - 2009

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

Our school dinners offer the same choice each day, and each day I try a new option. How long will it be before I eat the same meal again?

Weekly Problem 11 - 2009

Stage: 3 Short Challenge Level: Challenge Level:1

How many of the numbers 1 to 20 are not the sum of two primes?

Weekly Problem 13 - 2009

Stage: 3 Short Challenge Level: Challenge Level:1

How many zeros does 50! have at the end?

Weekly Problem 41 - 2009

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

At a cinema a child's ticket costs £$4.20$ and an adult's ticket costs £$7.70$. How much did is cost this group of adults and children to see a film?

Weekly Problem 45 - 2009

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

Flora has roses in three colours. What is the greatest number of identical bunches she can make, using all the flowers?

Weekly Problem 6 - 2010

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

Can you find three primes such that their product is exactly five times their sum? Do you think you have found all possibilities?

Weekly Problem 7 - 2010

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

Using the hcf and lcf of the numerators, can you deduce which of these fractions are square numbers?

Weekly Problem 22 - 2010

Stage: 3 Short Challenge Level: Challenge Level:1

Can you form this 2010-digit number...

Weekly Problem 30 - 2010

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Find out which two distinct primes less than $7$ will give the largest highest common factor of these two expressions.

Weekly Problem 48 - 2010

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

Tina has chosen a number and has noticed something about its factors. What number could she have chosen? Are there multiple possibilities?

Weekly Problem 5 - 2011

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Two numbers can be placed adjacent if one of them divides the other. Using only $1,...,10$, can you write the longest such list?

Weekly Problem 7 - 2011

Stage: 3 and 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

Roo wants to puts stickers on the cuboid he has made from little cubes. Will he have any stickers left over?

Weekly Problem 10 - 2011

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Will this product give a perfect square?

Weekly Problem 25 - 2011

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

Each time a class lines up in different sized groups, a different number of people are left over. How large can the class be?

Weekly Problem 5 - 2014

Stage: 3 and 4 Challenge Level: Challenge Level:1

Weekly Problem 5 - 2014

Weekly Problem 15 - 2014

Stage: 3 and 4 Challenge Level: Challenge Level:1

Weekly Problem 15 - 2014

Weekly Problem 26 - 2014

Stage: 3 and 4 Challenge Level: Challenge Level:1

Weekly Problem 26 - 2014

Weekly Problem 28 - 2014

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Weekly Problem 28 - 2014

Weekly Problem 39 - 2014

Stage: 3 and 4 Challenge Level: Challenge Level:1

Weekly Problem 39 - 2014

Weekly Problem 1 - 2015

Stage: 3 and 4 Challenge Level: Challenge Level:1

Weekly Problem 1 - 2015

Weekly Problem 4 - 2015

Stage: 3 and 4 Challenge Level: Challenge Level:1

Weekly Problem 4 - 2015

Weekly Problem 6 - 2015

Stage: 3 and 4 Challenge Level: Challenge Level:1

Weekly Problem 6 - 2015

Weekly Problem 33 - 2015

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Weekly Problem 33 - 2015